Autonomous Mobile Robots

Distributed Coordination in Swarms of Autonomous Mobile Robots

Based on materials by:

- Franck Petit

- Giuseppe Prencipe, University of Pisa - Nicola Santoro. Carlton University - Paola Focchini,

- P. Widmayer, - D. Peleg,

- X. Défago, JAIST

Mikaël Rabie

Mikael.rabie@lip6.fr

Setting and Motivations

Robot Swarms

Swarm: Collection of independent,

autonomously operating mobile robots

Robot Swarms

Swarm: Collection of independent,

autonomously operating mobile robots

Typically, the robots in a swarm are

➢ Very small

➢ Very simple

➢ Very limited in capabilities:

• Weak energy resources

• Limited means of communication Limited processing power

Why Multiple Robot Systems?

▪ Low cost: use several cheap & simple robots rather than single expensive one

▪ Can solve tasks impossible for a single robot (e.g., sweep large regions)

▪ Can perform risky / hard tasks in hazardous / harsh environments

▪ Can tolerate destruction of some robots

▪ Applications:

➢ Military operations

➢ Space explorations

➢ Search&rescue missions

➢ Toxic spill cleanups

➢ Fire fighting

➢ Risky area surrounding or surveillance

➢ Exploration of awkward environments

➢ Large-scale construction

➢ Environmental monitoring

Specific Tasks for Swarms

▪ Movement management

▪ Movement limitation

▪ Collision avoidance

▪ 2D/3D settings

▪ Complex coordination operations

▪ Global control

Most previous work:Centralized control, suitable for small robot team, inadequate for large swarms

➙ Distributed control:

▪ No central coordination

▪ Scalability

Setting

Distributed System whose

Entities

simple

(

robots

Motorial

Freely move on a 2 (or 3) dimensional environment

Sensorial

Sense the positions of the others in the environment

Why study oblivious (& relatively dumb)

robots?

❑ Algorithms that work correctly for weaker

❑ Algorithms will work in a dynamic environment (where robots

join/leave the system)

❑ The system can start in (almost) any

configuration

However….

• Many simple units

– Not expensive – Modular

– Fault tolerant

• Few complex specialized units

– Expensive

– Not fault tolerant

Problem:

Coordinate them

The Problem

General aim of the study

• Which are the elementary tasks that can be achieved deterministically?

• What are the

for this?

• Given a task, what kind of

is necessary so that the robots can accomplish it (

)?

Analyze from an algorithmic point of view the distributed control of a set of autonomous mobile robots

Problem

Analysis of minimum level of capabilities (sensorial, computational, and motorial) robots must possess to COLLECTIVELY solve a given task.

For globally accomplishing a given task: how "weak" can each single robot be?

How much local power is necessary to perform global computations?

Cooperative Primitive Tasks

Gathering Alignment

Other Patterns Circle Formation

Election

Approaches

Previous and Related Work

• Fukuda et al, 1989 (CEBOT)

• Brooks, 1985

• Mataric, 1994

• Cao at al, 1995 (survey)

• Durfee, 1995

• Balch and Arkin, 1998

Previous Work

(Algorithmic approaches)

Provably correct solutions

Termination in finite time

Very few works ...

(Robotics, AI)

Heuristic solutions

Convergence to solution

Tipically...

The Algorithmic Approach

Study under what conditions on the robots’ capabilities a given global task is solvable in finite time.

Find Algorithmic solutions

The Model

Environment

Infinite Plane

Environment

Finite Graph (Discrete Env.) Infinite Plane

The Model

(Yamashita et al., SIROCCO 1996)

• Homogeneous

• Anonymous

• Autonomous

• Mobile

• Deaf and Dumb _x

y

Unit

Algorithm:

1.

2.

3.

….

Sensors

No explicit

communication

-Assumptions on Robots’ power- Agreement on Coordinate System

x y

x

y x

y x y

Total agreement

x

x

x x

Agreement on one axis

direction and orientation Agreement on directions

x y

x y

x y

x x y

y

- Assumptions on Robots' power -

No Agreement

Models of Orientation

Full-compass: Axes and polarities of both axes.

Half-compass: Both axes known, but positive polarity of only one axis (in other axis, robots may have

different views of positive direction).

Direction-only: Both axes, but not polarities.

Axes-only: Both axes, but not polarities. In addition, robots disagree on which axis is x and which is y.

No-compass: No common orientation information.

Note: In general, robots do not share common unit distance or

- Assumptions on Robots' Power - Radius of Visibility: Limited /Unlimited

V

- Assumptions on Robots' Power - Oblivious/Non Oblivious

Non-Oblivious:

computation

Oblivious:

Modeling Movements

Assumption 1

The maximum distance

r

Assumption 2

There is a lower bound d_r>0 on the distance a robot

r

unless its destination is closer than d_r>0.

Modeling The Time

• A critical aspect in every distributed system is the time

– Synchronous?

– Asynchronous?

• At the beginning the proposed model for robots was basically synchronous (SYNC, SSYNC, SYm)

– Semi-synchronous – Fully-synchronous

Instantaneous Actions of SYm

Suzuki et al., 1996

Discrete Time 0,1,...

At each time instant

t

r

Active

Inactive

At least one Active robot at each time instant, and every robot is Active infinitely often

Instantaneous Actions of SYm

Suzuki et al., 1996

LOOK

COMPUTE MOVE

Phases of an Active robot t

t+1

Instantaneous Actions of SYm

Suzuki et al., 1996

LOOK

Visibility:

Unlimited Limited

Uses its sensors

to observe the world.

result = SNAPSHOT of the world

COMPUTE MOVE

t

t+1

Instantaneous Actions of SYm

Suzuki et al., 1996

MOVE

LOOK

COMPUTE

input = positions of the robots result = destination point p

Oblivious:

positions of the robots retrieved in the last Look

Non Oblivious:

positions of the robots since the beginning

Execute algorithm,



t

t+1

Instantaneous Actions of SYm

Suzuki et al., 1996

LOOK

COMPUTE MOVE

The robot moves towards the computed destination

t

t+1

Instantaneous Actions of SYm

Suzuki et al., 1996

LOOK

COMPUTE MOVE

p

(t)

r

t

For all

t0

r

p

(t+1)=p

(t) r

p

(t+1)=p

p: point returned by



r

atomically!

t

t+1

Asynchronicity

• In 1999 asynchronicity was introduced in the model

– CORDA or ASYNC

The Life Cycle (Corda)

LOOK

COMPUTE

MOVE WAIT

The Life Cycle (Corda)

LOOK

COMPUTE

MOVE WAIT

Visibility:

Unlimited Limited

Uses its sensors

to observe the world.

result = SNAPSHOT of the world

The Life Cycle (Corda)

LOOK

COMPUTE

MOVE WAIT

input = position of the other robots result = destination

point Obliviousness:

The local computation is based solely on what the robot has just observed

The Life Cycle (Corda)

LOOK

COMPUTE

MOVE WAIT

The robot moves towards the

computed

destination (it might not reach it)

The movement is non-instantaneous.

The Life Cycle (Corda)

LOOK

COMPUTE

MOVE WAIT

No Global Clock

No Synchronization…

But cannot wait forever To take into account

asynchronous behavior.

Sym vs CORDA

SYm

• Instantaneous actions.

CORDA

• Full asynchronicity.

Instantaneous Actions in SYm

t+1

COMPUTE

LOOK MOVE

Asynchronicity in Corda

t

Asynchronicity in Corda

A robot could see other robots while they move !

A robot cannot distinguish between moving robots and waiting robots !

t’

Timing Models

ASYNC (CORDA) -Fully asynchronous

[Flocchini et. Al, 1999]

Arbitrary & varying operation rates and delays

SSYNC (Sym) - Semi-synchronous

[Suzuki+Yamashita, 1996]

Fixed time cycles, but robots may be active / inactive

FSYNC - Fully synchronous

Fixed time cycles, all robots active in every cycle

Corda vs. SYm

Problem P solvable in Corda

P solvable in SYm

Corda vs. SYm

Problem P unsolvable in Corda

P unsolvable in SYm